Problem: $ B = \left[\begin{array}{rrr}4 & 0 & 2 \\ 1 & -2 & -2\end{array}\right]$ $ F = \left[\begin{array}{rrr}3 & -1 & 2 \\ 3 & 2 & -1\end{array}\right]$ Is $ B+ F$ defined?
Solution: In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ B$ is of dimension $( m \times  n)$ and $ F$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ B$ ) must equal $ p$ (number of rows in $ F$ ) and 2. $ n$ (number of columns in $ B$ ) must equal $ q$ (number of columns in $ F$ Do $ B$ and $ F$ have the same number of rows? Yes Yes No Yes Do $ B$ and $ F$ have the same number of columns? Yes Yes No Yes Since $ B$ has the same dimensions $(2\times3)$ as $ F$ $(2\times3)$, $ B+ F$ is defined.